Answer
$xe^{x}-e^{x}+C$
Work Step by Step
We use the formula
$\int udv=uv-\int vdu$
with $u=x$, $dv=e^{x}dx$
$du=dx$, $v=e^{x}$
Then $\int xe^{x}dx=x\times e^{x}-\int e^{x}dx$
$=xe^{x}-e^{x}+C$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 8: Techniques of Integration - Section 8.2 - Integration by Parts - Exercises 8.2 - Page 455: 7
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